CME 211: Homework 3


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CME 211: Homework 3

This assignment was designed by Patrick LeGresley and modified for the purposes of this course.
Wing design might begin with the analysis and design of one or more airfoils, the 2D cross sections of a wing.
Airfoils could be tested experimentally in a wind tunnel or via computer simulation using Computational Fluid
Dynamics (CFD) to gather information about the pressure distribution, often expressed as the non-dimensional
pressure coecient (Cp) as shown in Figure 1.
CME$211$/$EARTHSCI$211 Fall$2014
Assignment 3
Due:$October$17,$2014 at$2$pm
Wing%design might$begin with$the$analysis$and$design$of$one$or$more$airfoils,$the 2D$cross$
sections of$a$wing.$$Airfoils$could be$tested$experimentally$in$a$wind%tunnel or$via$computer
simulation$ using$ Computational% Fluid% Dynamics (CFD)$ to$ gather$ information$ about$ the$
pressure$ distribution,$ often$ expressed$ as$ the$ nonOdimensional$ pressure% coefficient (Cp)$ as$
Figure%1:%Pressure%coefficient%distribution%around%the%RAE 2822%airfoil
the$nonOdimensional$lift coefficient.$$This$can$be accomplished$by:
1.$Computing the$chord$length$(see$Figure$2)$as$the$distance$from$the$leading$edge$
to$ the$ trailing$ edge$ of$ the$ airfoil.$ $ The$ chord$ length$ will$ later$ be$ used$ to$ nonO
2.$ The$ airfoil$ geometry$ is$ defined$ by$ a$ series$ of$ points.$ $ Each pair$ of$ consecutive$
points can$ be$ considered$ to$ be$ connected$ by$ a$ straight$line$ that$ forms$ a$ panel$ as$
and the$nonOdimensional$force$acting$perpendicular$to$a panel$can$be$computed$by$
multiplying$the$pressure$coefficient$by$the$panel$length nonOdimensionalized$by$the$
chord$length.$$This$nonOdimensional$force$acting$perpendicular$to$a panel$can$then$
be$decomposed$into$components$in$the$Cartesian$directions,$∆!! and ∆!!,$as$shown$
Dynamic Domain Decomposition and Error Correction
for Reduced Order Models
−0.5 0 0.5 1 1.5 −0.5
Patrick A. LeGresley and Juan J. Alonso
Dept. of Aeronautics & Astronautics
Stanford University
41st Aerospace Sciences Meeting
Reno, Nevada
January 6, 2003
AIAA 2003-0250 1
Figure 1: Pressure coecient distribution around the RAE 2822 airfoil
The pressure coecient distribution can be integrated over the airfoil surface to determine the non-dimensional
lift coecient. This can be accomplished by:
1. Computing the chord length (see Figure 2) as the distance from the leading edge to the trailing edge of
the airfoil. The chord length will later be used to non-dimensionalize the airfoil geometry.
2. The airfoil geometry is defined by a series of points. Each pair of consecutive points can be considered
to be connected by a straight line that forms a panel as shown in Figure 3. The pressure coecient
data is available for each of these panels and the non-dimensional force acting perpendicular to a panel
can be computed by multiplying the pressure coecient by the panel length non-dimensionalized by
3.$The$nonOdimensional$force$contributions$summed$over$all$of$the$panels$yield the$
total Cartesian$ force$ coefficients cx and$ cy.$ $ Note$ that$ when$ you$ sum$ the$
contributions$ you$ will$ need$ to$ be$ careful$ about$ the$ sign$ of$ the$ contribution$
4.$ And$ finally the$ lift$ coefficient, which$ is$ the$ nonOdimensional$ force$ component$
!! = !! cos ! − !! sin !
where$ the$ flow$ velocity$ goes$ to$ zero.$ $ The$ stagnation$ point$ corresponds$ to$ a$ pressure$
coefficient$of$1.0$and$an$airfoil$would$typically$have$a stagnation$point$somewhere$near the$
Figure%2:%Relationship between%flow%direction%and%lift%direction
Figure%3:%Projecting%pressure%into%x%and%y%components on%one%panel%of%the%airfoil
Figure 2: Relationship between flow direction and lift direction
the chord length. This non-dimensional force acting perpendicular to a plane can then be decomposed
into components into the Cartesian directions, cx and cy, as shown in Figure 3.
3. The non-dimensional force contributions summed over all the of the panels yield the total Cartesian
force coecients cx and cy. Note that when you sum the contributions you will need to be careful about
the sign of the contribution depending of whether it is in the positive or negative x or y direction.
4. And finally the lift coecient, which is the non-dimensional force component perpendicular to the flow
direction, can be computed as:
cl = cy cos – ≠ cx sin –
Other interesting characteristics of the flow could include identify the stagnation point(s) where the flow
velocity goes to zero. The stagnation point corresponds to the pressure coecient of 1.0 and an airfoil would
typically have a stagnation point somewhere near the leading edge.
Figure 3: Relationship between flow direction and lift direction
This assignment requires that you have completed CME211 HW0. If you have not completed
HW0, please do so (even if it is past the HW0 deadline). Part of HW0 is the creation of your homework
repository, which will be used throughout the quarter. You will not be able to complete HW3 (or any future
CME211 homework) without completing HW0.
These instructions assume that you are logged into and have cloned your CME211
homework repository to your Farmshare user directory. First, navigate to your homework repository:
$ cd /farmshare/user_data/[sunet_id]/cme211-[github_user]
$ ls STUDENT hw0 hw1 hw2
In the above cd command, [sunet_id] must be replaced with your SUNetID and [github_user] must be
replaced with your GitHub username.
At this point, it is good to check if your local repository is clean and up-to-date with the remote repository
on GitHub. This is achieved by running:
$ git status
On branch master
Your branch is up-to-date with origin/master.
nothing to commit, working directory clean
If you get a dierent message, make sure to commit (or revert) all modified files or perform a $ git pull to
retrieve remote changes. Now, create a hw3 directory (it must be lower case):
$ mkdir hw3
$ ls STUDENT hw0 hw1 hw2 hw3
Now, create a basic README inside of hw3, commit it to the repository, and push to GitHub:
$ emacs hw3/README
# add some basic info to the README
# check status of the repo with $ git status
$ git add hw3
$ git commit -m “add hw3 readme”
# … output omitted …
$ git push origin master
# … output omitted …
All HW3 files must go inside of the hw3 directory you just created. So, $ cd hw3 and you are ready to go.
Scoring: (60 points functionality, 20 design, 10 style, 10 writeup)
In this assignment you will use Object Oriented Programming (OOP) concepts to create an Airfoil class
that will handle the loading and basic processing of data associated with an airfoil at multiple angles of
attack. Each of the provided directories naca0012/ and naca2412/ contain data for one airfoil.
The main program that will invoke your Airfoil class has already been written in the provided file
that you should not change:
import sys
import airfoil
if len(sys.argv) < 2:
print( python3 {} <airfoil data directory>.format(sys.argv[0]))
inputdir = sys.argv[1]
a = airfoil.Airfoil(inputdir)
except RuntimeError as e:
print(ERROR: {}.format(e))
A data directory, such as naca0012, is provided to the program via the command line arguments and used
to instantiate an instance of your Airfoil class. Using print on the resulting instance of the class should
summarize the test data as shown here:
$ python naca0012/
Test case: NACA 0012
alpha cl stagnation pt
—– ——- ————————–
-3.00 -0.3622 ( 0.0030, 0.0094) 0.9906
0.00 0.0000 ( 0.0000, 0.0000) 0.9944
3.00 0.3622 ( 0.0030, -0.0094) 0.9906
6.00 0.7235 ( 0.0099, -0.0170) 0.9967
9.00 1.0827 ( 0.0219, -0.0246) 0.9977
The summary shows the lift coecient for each angle of attack and the (x, y) location and pressure coecient
for the stagnation points. Note that there may not be a point with a pressure coecient of exactly 1.0 so you
should return the panel value closest to 1.0 and an (x, y) coordinate that is the average of the points defining
that particular panel.
Design Requirements & Considerations
How you implement your Airfoil class is largely up to you. However there are a few constraints and
1. You are not allowed to modify the file. So your class will need to be instantiated via the name
of a directory containing airfoil data, and it needs to implement the string representation method such
that the output of the program is consistent with the example shown above.
2. Think about the OOP concepts discussed in lecture and implement your class in terms of multiple
methods. Splitting it up into about 6 methods would be appropriate. Be sure to provide a document
string for each method, plus one for the class as a whole.
3. It is important to provide clear, easily understandable feedback when errors exist in input data. In this
assignment, you are required to generate RuntimeError exceptions with understandable messages in
the following cases:
• the argument to airfoil.Airfoil() is not a valid directory
• any of the required data files cannot be found in the data directory
• an error is detected in reading an input file
Raising a RuntimeError
It is simple to raise a RuntimeError in Python:
raise RuntimeError(“error message goes here”)
A RuntimeError is a built-in Python exception type for runtime errors.
File formats
In each airfoil directory there should be one xy.dat containing the (x, y) coordinates for the panels that
define the airfoil geometry and multiple data files such as alpha0.0.dat, alpha+3.0.dat, etc. that contain
pressure coecient data for one angle of attack such as 0.0 degrees, +3.0 degrees, etc. as encoded within the
A quick inspection of the first 5 lines of the data files with the unix head command shows:
$ head -n 5 naca0012/xy.dat
NACA 0012
1.000000 0.1260000E-02
0.9916770 0.2421811E-02
0.9803640 0.3982079E-02
0.9672594 0.5762782E-02
$ head -n 5 naca2412/alpha+3.0.dat
# Cp
The first line of the xy.dat file contains the name of the airfoil, followed by the lines containing the x and y
coordinates for each of the points that define the panels. Points start at the trailing edge (approximately
x = 1.0), proceed along the upper surface to the leading edge (approximately x = 0.0), and then along the
lower surface back to the trailing edge again (counter-clockwise around the airfoil).
For the pressure coecient files, the filenames should be of then form alpha<angle of attack>.dat, e.g. the
alpha+3.0.dat has an angle of attack of +3.0 degrees. Note that your program should robustly handle input
files with diering angles of attack. Within each file the first line is a header and then each line contains the
pressure coecient for one panel. The first value is for the first panel (defined by the first and second points),
the second value is for the second panel (defined by the second and third point), and so on. So given the
order of the points the panels start at the trailing edge, go along the upper surface to the leading edge, and
then back to the trailing edge.
You may find the glob.glob() function to be useful for determining which pressure coecient files are
present in the data directory, and the functions from os.path for working with file paths, and testing for the
presence of directories and files:
Disallowed Imports
Please do not use any module from the following set: csv, numpy, pandas, tabular, statistics. If you have
a question about whether you may use a particular module, please post on Canvas. In general, we’d like you
to implement your solution using the fewest dependencies as possible; we recommend sticking with glob,
math, os, and sys for this assignment.
Error Handling
This is the first assignment that we ask you to consider handling runtime errors gracefully. The program we
ask you to write depends on a set of well-formatted input files being present. What happens if (some of)
these files are non-existent or malformed, can your program handle such cases? What if the input-directory is
specified with or without a trailing delimiter? We don’t ask that you bullet proof your program against the
universe of possible errors, but we do ask that you consider a few dierent cases of errors or variations in
inputs that could arise, and write (error handling) code accordingly.
The computation that is required for this assignment is quite trivial, and your programs should run in a split
second for any set of input files we provide. You do not need to consider how your program would scale to
handle larger inputs.
Learning Goals
This assignment packs in a lot. We will not only implement our own module and class, complete with a
private method, but we will also consider how to incorporate error handling into our program. After the
assignment, we will have a stronger appreciation for what it means to decompose a complex program into
reliable and robust individual pieces.
In your hw3/README file, provide a description of your code design to someone who has never read this
assignment handout. Be sure to explain how the design illustrates key OOP concepts such as abstraction, decomposition, and encapsulation. Also describe what error checking and exception generation you incorporated
into your class implementation.
Checklist & submission
The following files must be present in the hw3 directory of your CME211 GitHub homework repository by
the deadline:
• README: text document with answers to questions from the assignment. You may also call this file
README.txt or (if you want to use Markdown formatting).
• the Python script listed above to drive the program. Note you must use exactly as
• Python module containing your Airfoil class definition.
• Do not commit naca2412/ or naca0012/ data directories or other data files to your repository. We will deduct points if extraneous data files are present in your repository.
• Take care to follow the file and directory names exactly. Everything is case sensitive.
• Please avoid committing other data or temporary files to the repository. We only want to see your
README file and Python code.
• Your homework is not complete until you have pushed the above files to GitHub.
• Late work is not accepted.
• Do regular commits when you have finished little pieces of the puzzle. Don’t do a commit for small
individual changes, but also don’t make only one huge commit. There’s no set rule for when to commit.
Whenever you feel the need to ‘save’ your (good) progress, think about committing.
• When you do a commit, type a sensible commit message such that your repository’s commit log makes
sense to an outsider, for tracking what you have done. This is very important if you work with a team
on the same code.

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